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Q34 What is the coefficient of correlation from the following data:
X: 1 2 3 4 5
Y: 5 4 3 2 6
A) 0 B) -0.75 C) -0.85 D) 0.82?
X: 1 2 3 4 5
Y: 5 4 3 2 6
A) 0 B) -0.75 C) -0.85 D) 0.82?
Most Upvoted Answer
Q34 What is the coefficient of correlation from the following data: X:...
Calculation of Coefficient of Correlation
- To calculate the coefficient of correlation, we first need to find the mean of X and Y.
- Mean of X (X̅) = (1+2+3+4+5)/5 = 3
- Mean of Y (Y̅) = (5+4+3+2+6)/5 = 4
Calculating the covariance
- Covariance (Sxy) = Σ((X - X̅)(Y - Y̅)) / n
- Sxy = ((1-3)(5-4) + (2-3)(4-4) + (3-3)(3-4) + (4-3)(2-4) + (5-3)(6-4)) / 5
- Sxy = (-2*1 + -1*0 + 0*-1 + 1*-2 + 2*2) / 5
- Sxy = (-2 - 0 + 0 - 2 + 4) / 5
- Sxy = 0
Calculating the standard deviation
- Standard deviation of X (Sx) = √(Σ(X - X̅)² / n)
- Sx = √(((1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²) / 5)
- Sx = √((4 + 1 + 0 + 1 + 4) / 5)
- Sx = √(10 / 5)
- Sx = √2
- Standard deviation of Y (Sy) = √(Σ(Y - Y̅)² / n)
- Sy = √(((5-4)² + (4-4)² + (3-4)² + (2-4)² + (6-4)²) / 5)
- Sy = √((1 + 0 + 1 + 4 + 4) / 5)
- Sy = √(10 / 5)
- Sy = √2
Calculating the coefficient of correlation
- r = Sxy / (Sx * Sy)
- r = 0 / (2 * 2)
- r = 0
Therefore, the coefficient of correlation from the given data is 0. This means that there is no linear relationship between X and Y.
- To calculate the coefficient of correlation, we first need to find the mean of X and Y.
- Mean of X (X̅) = (1+2+3+4+5)/5 = 3
- Mean of Y (Y̅) = (5+4+3+2+6)/5 = 4
Calculating the covariance
- Covariance (Sxy) = Σ((X - X̅)(Y - Y̅)) / n
- Sxy = ((1-3)(5-4) + (2-3)(4-4) + (3-3)(3-4) + (4-3)(2-4) + (5-3)(6-4)) / 5
- Sxy = (-2*1 + -1*0 + 0*-1 + 1*-2 + 2*2) / 5
- Sxy = (-2 - 0 + 0 - 2 + 4) / 5
- Sxy = 0
Calculating the standard deviation
- Standard deviation of X (Sx) = √(Σ(X - X̅)² / n)
- Sx = √(((1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²) / 5)
- Sx = √((4 + 1 + 0 + 1 + 4) / 5)
- Sx = √(10 / 5)
- Sx = √2
- Standard deviation of Y (Sy) = √(Σ(Y - Y̅)² / n)
- Sy = √(((5-4)² + (4-4)² + (3-4)² + (2-4)² + (6-4)²) / 5)
- Sy = √((1 + 0 + 1 + 4 + 4) / 5)
- Sy = √(10 / 5)
- Sy = √2
Calculating the coefficient of correlation
- r = Sxy / (Sx * Sy)
- r = 0 / (2 * 2)
- r = 0
Therefore, the coefficient of correlation from the given data is 0. This means that there is no linear relationship between X and Y.
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Q34 What is the coefficient of correlation from the following data: X: 1 2 3 4 5 Y: 5 4 3 2 6 A) 0 B) -0.75 C) -0.85 D) 0.82?
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Q34 What is the coefficient of correlation from the following data: X: 1 2 3 4 5 Y: 5 4 3 2 6 A) 0 B) -0.75 C) -0.85 D) 0.82? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q34 What is the coefficient of correlation from the following data: X: 1 2 3 4 5 Y: 5 4 3 2 6 A) 0 B) -0.75 C) -0.85 D) 0.82? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q34 What is the coefficient of correlation from the following data: X: 1 2 3 4 5 Y: 5 4 3 2 6 A) 0 B) -0.75 C) -0.85 D) 0.82?.
Q34 What is the coefficient of correlation from the following data: X: 1 2 3 4 5 Y: 5 4 3 2 6 A) 0 B) -0.75 C) -0.85 D) 0.82? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q34 What is the coefficient of correlation from the following data: X: 1 2 3 4 5 Y: 5 4 3 2 6 A) 0 B) -0.75 C) -0.85 D) 0.82? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q34 What is the coefficient of correlation from the following data: X: 1 2 3 4 5 Y: 5 4 3 2 6 A) 0 B) -0.75 C) -0.85 D) 0.82?.
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